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Solving algebraic problems in history and in the classroom
Vojáček, Josef ; Kvasz, Ladislav (advisor) ; Zamboj, Michal (referee)
This diploma thesis deals with the comparison of historical solutions of word problems with student solutions. Its aim was to describe how students solve historical word problems, while looking for analogies between student and historical solutions. This intention led me to a better understanding of student solutions. The theoretical part of the thesis describes important concepts for algebraic word problems, such as a variable, algebraic expression or algebraic word problem. In the historical part I describe chronologically the development of algebra from antiquity through the Middle Ages and the Renaissance to the Baroque. In each period, I mention important mathematicians of the time and present several solved word problems. In most cases, I analyze these solutions from the perspective of today's mathematics. The theoretical part describes the research that took place at the eight-year grammar school. As part of the research, I gave students 6 historical tasks across historical periods and then analyzed the ways in which students solved problems. I found that for most of the tasks, there were solutions similar to the historical solutions among the student's solutions. Some historical methods appeared very often. An example is the use of addition instead of multiplication, or division, as used by the...
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